To be fair, you'd have to assume that the two aircraft were being flown by pilots of equal skill and experience. The two models that it is most fair to compare would be the Spitfire XIV and P-51D, which were the primary models in service with their respective services in mid-1944. The Spitfire XIV actually entered service in January 1944, five months before the P-51D. The Spitfire XIV was faster than the Mustang, more maneuverable, had a higher service ceiling, could climb better, and even had a better rate of roll, which was formerly the Mustang's only performance advantage over the Spitfire. It was superior to the P-51D in EVERY combat category except initial dive speed and range, and the only way range came into play in a dogfight is if the P-51 could fly around long enough for the Spit to run out of fuel!
Some quotes: William Dunn (US fighter ace who flew Spitfires, P-51s, Hurricanes, and P-47s): "Now, if I had to make the choice of one fighter aircraft above all the others - one that I'd rather have tied to the seat of my pants in any tactical situation - it would be, without any doubt, the world's greatest propeller driven flying machine - the magnificent and immortal Spitfire."
Eric Brown (RN test pilot and holder of the world record for number of types of aircraft flown): "I have flown both for many hours, and would choose the Spitfire [over the Mustang] if given a choice in a fight to the death."
Writer Jerry Scutts, quoting German pilots in his book JG 54: "The Jagflieger had to keep a wary eye out for enemy fighters, particularly Spitfires, a type JG 54's pilots had developed a particular aversion to...Pilot reflections do not, surprisingly enough, reflect over-much respect for the Mustang or Lightning, both of which the Germans reckoned their Fockes were equal to - unless they were met in substantial numbers."
Gordon Levitt, Israeli fighter pilot, comparing the Spitfire, Mustang, and Avia S-199 (Jumo-engined
Bf 109), all of which the Israelis flew: "Despite the pros and cons, the Spitfire was everyone's first choice."
Karl Stein, Luftwaffe Fw 190 pilot (who served mainly on the Eastern front): "English and American aircraft appeared on the scene in those closing days of the European war. Spitfires were the most feared, then Mustangs..."
USAAF 31st FG War Diary (when transferring from Spitfires to P-51s): "Although pilots think that the P-51 is the best American fighter, they think the Spitfire VIII is the best fighter in the air."
USAAF pilot Charles McCorkle (who flew both in combat), reporting on a mock combat between a Spitfire and Mustang in 1944: "Now we could see which was the better aircraft...a Mustang and a Spit took off for a scheduled 'combat', flown by two top young flight commanders. When the fighters returned, the pilots had to agree that the Spitfire had won the joust. The Spit could easily outclimb, outaccelerate, and outmaneuver its opponent..." The Mustang was a great fighter, but it was great because it had the range the Spitfire lacked, enabling it to take the fight to the enemy. But in a one-on-one dogfight, there's absolutely no comparison. The Spitfire would win decisively, 99 times out of 100...